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VCE Maths Methods Unit 1-4: Trigonometry (circular function)

Become more proficient and confident in trigonometry (circular functions) so that you can ace your Maths Methods exam!

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Be familiar with the three trigonometric ratios and the way they are calculated: sine = opposite/hypotenuse [SOH], cosine = adjacent/hypotenuse [CAH], tangent = opposite/adjacent [TOA]

Have a basic understanding of Pythagoras’ theorem (a^2 + b^2 = c^2), which is useful to help understand the derivations of some of the trigonometric formulae

Description

After going through this course, you will be able to understand how trigonometry (circular functions) works at an Australian VCE Maths Methods Units 1-4 level, and apply such knowledge on exam questions. Each lecture includes many clearly annotated diagrams to make mathematical concepts easier to understand, and will be followed by a quiz to test your understanding.

The lectures are designed to cater for both unit 1/2 students and unit 3/4 students, with unit 1/2 and unit 3/4 content indicated in the ‘lecture description’ and the beginning of each lecture. Unit 1/2 students only need to watch the unit 1/2 content of each lecture, although you may go on to watch the unit 3/4 content if you want to get a head start. Unit 3/4 students may find the unit 1/2 content a good revision for them.

You are encouraged to go through the lectures in order since the content from the earlier lectures is often required in the later lectures.

Who is the target audience?

This course mainly caters for students doing the Australian VCE subject, Mathematical Methods unit 1/2 and 3/4.

However, students from other countries or Australian states at a level equivalent to year 11 and 12 in Australia may also find this course useful.

This course will clearly outline the content from unit 1/2 and unit 3/4, although sometimes there is a slight overlap between the two. For unit 1/2 students, you can also watch the unit 3/4 content to get a head start for the future; while for unit 3/4 students, you can also watch the unit 1/2 content if you need some revision on the previously learnt material.

Note: This lecture does not include the derivations on the basic exact trigonometric values and the symmetry formulae. For a look at these derivations (which is not examinable in the VCE exam, but is useful knowledge nevertheless), refer to lectures 8 and 9 under the "additional resources" section.

Evaluating exact trigonometric values

12:08

Evaluating the exact trigonometric values

3 questions

Content:

- Rules to solve trigonometric equations [unit 1/2]

- More complicated examples [unit 3/4]

- Solving for the general solution [unit 3/4]

Solving trigonometric equations

13:24

Solving trigonometric equations

2 questions

Content:

- The basic shape of sine and cosine graphs [unit 1/2]

- Determining the shape, mean value, amplitude and period [unit 1/2]

- Sketching the graph (without horizontal translation) [unit 1/2]

- Sketching the graph (with horizontal translation) [unit 3/4]

Sketching sine and cosine graphs

09:40

Sketching sine and cosine graphs

3 questions

Content:

- The basic shape of tangent graphs [unit 1/2]

- Determining the shape, mean value and period [unit 1/2]

- Sketching the graph (without horizontal translation) [unit 1/2]

- Sketching the graph (with horizontal translation) [unit 3/4]

Sketching tangent graphs

11:05

Sketching tangent graphs

2 questions

We will go through a worded problem (on the Ferris wheel!) together in this lecture, which is divided into parts a, b, c, d and e. This question is more suitable for students in units 3/4, although students in unit 1/2 may attempt this question if they want to challenge themselves a bit.

Applications on trigonometry

13:01

Applications on trigonometry

2 questions

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Additional resources

2 Lectures
10:00

We are going to derive all the basic exact trigonometric values included in lecture 3 by drawing a few triangles. Watch out this interesting video to find out!

We are going to show you why you have 'A-S-T-C' in the unit circle (which relates to the symmetry formulae included in lecture 3). If this doesn't make sense to you, I would suggest you to watch lecture 3 first!

I am a 1st year medical student in the University of Melbourne (as of 2017), and I have completed three years of Bachelor of Biomedicine. I have had three years of experience providing one-on-one maths tutoring at an Australian year 11-12 level, for the subjects of Maths Methods and Specialist Maths. When tutoring, I like to explain the steps that lead to the final answer in a clear and logical manner, and I try to make my lessons as engaging as possible. I have used the same style of tutoring my students Maths Methods in these videos, so I hope you find them highly useful!